They're the things that hang off your shirt by your shoulders. You're supposed to put your arms in them.

When it comes to ink work, "sleeves" are the lovely description of a person's arms which are almost completely covered with tattoos from the shoulders down to the wrists. Giving the shirtless person the look of having only "sleeves" on, and no shirt. Basically, the tattoos cover where your long sleeved shirt covers. This way, a person who wants a LOT of tattoos, can do just that, and yet wear a long sleeved shirt, and still have them covered for work.